Advertisements
Advertisements
प्रश्न
Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.
Advertisements
उत्तर
In ΔABC and ΔPQR
BC = QR
AD and PM are medians of BC and QR respectively
⇒ BD = DC = QM = MR
In ΔABD and ΔPQM
AB = PQ
D = PM
BD = QM
Therefore, ΔABD ≅ ΔPQMABD PQM ...(SSS criteria)
Hence, ∠B = ∠Q
Now in ΔABC and ΔPQR
AB = PQ
BC = QR
∠B = ∠Q
Therefore, ΔABC ≅ ΔPQRABC PQR. ...(SAS criteria)
APPEARS IN
संबंधित प्रश्न
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =
In the following example, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
Δ ABC ≅ ΔPQR
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
In the given figure, prove that: ∆ ABD ≅ ∆ ACD
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
∆ABC and ∆PQR are congruent under the correspondence:
ABC ↔ RQP
Write the parts of ∆ABC that correspond to
(i) `bar"PQ"`
(ii)∠Q
(iii) `bar"RP"`
If AB = QR, BC = PR and CA = PQ, then ______.
